The best closest daytrip from Las Vegas is out to Red Rock Canyon, a mere 20 miles west on W. Charleston from Las Vegas Blvd. South. It's a 64,000-acre BLM park that showcases some spectacularly colorful sandstone (emblematic of the U.S. Southwest). It costs $5 to enter. There's a 13-mile loop road, with a long day's worth of hiking, rock scrambling, bouldering, climbing, photographing, picnicking, etc. We've published a couple of hiking guides to Las Vegas and Southern Nevada that contain lots of hikes and climbs at Red Rock (go to www.greatstuff4gamblers.com and search for Hiking Las Vegas and/or Hiking Southern Nevada. You owe it to yourself to slip the grip of the Strip at least once during your trip -- and Red Rock should be your first stop.
If you have a little extra time after you're done with Red Rock, continue west on NV Rte. 159 (which W. Charleston turns into) to Spring Mountain State Park, which occupies a gorgeous valley below the sheer eastern escarpment of the mighty Spring Mountains that hem in Las Vegas Valley on the west. Tour the ranch house; take a guided hike around the grounds; bring a frisbee or a ball of some kind to spend some quality outdoor time in a scenic wonderland a mere half-hour from the Strip.